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AP Calculus BC
- By Dr.Karatas
Overview:
The AP Calculus BC course builds upon the concepts covered in AP Calculus AB, delving deeper into both differential and integral calculus. This course extends students’ understanding of calculus through additional topics such as parametric, polar, and vector functions, as well as series and sequences. Students will explore advanced calculus techniques and applications, preparing them for higher-level mathematics courses in college.
Skills to Learn:
- Advanced problem-solving skills in calculus, including techniques for solving more complex problems
- Proficiency in applying calculus concepts to a wide range of mathematical and real-world scenarios
- Understanding of advanced calculus topics such as parametric, polar, and vector functions, as well as series and sequences
- Ability to analyze functions and their behavior in various coordinate systems
Prerequisites:
- Successful completion of an AP Calculus AB course or equivalent knowledge of calculus concepts covered in AP Calculus AB
- Strong algebraic skills, including familiarity with polynomial, exponential, logarithmic, and trigonometric functions
- Solid understanding of limits, derivatives, and integrals, as well as their applications
- Proficiency in manipulating equations and solving equations involving calculus techniques
Curriculum:
1- Advanced Differentiation and Integration:
- Advanced techniques for differentiation (implicit differentiation, logarithmic differentiation)
- Applications of differentiation (curve sketching, motion problems)
- Advanced techniques for integration (integration by partial fractions, trigonometric substitution)
2- Parametric, Polar, and Vector Functions:
- Parametric equations and their derivatives
- Polar coordinates and polar functions
- Vector-valued functions and their derivatives
3- Infinite Series and Sequences:
- Convergence and divergence of infinite series
- Tests for convergence (comparison test, ratio test, integral test)
- Power series and Taylor series expansions
4- Differential Equations and Mathematical Modeling:
- Solutions of higher-order differential equations
- Modeling with differential equations (population growth, Newton’s law of cooling)
- Systems of differential equations and their applications
5- Advanced Applications of Integration:
- Arc length and surface area of curves and surfaces
- Volume by slicing, cylindrical shells, and other methods
- Applications to physics, engineering, and other fields
6-Exam Preparation:
- Practice with multiple-choice and free-response questions specific to AP Calculus BC
- Test-taking strategies and tips for success on the AP Calculus BC exam
- Similar to AP Calculus AB, students will engage in interactive activities, problem-solving exercises, and real-world applications to deepen their understanding of advanced calculus concepts and their practical significance.
Who: 10,11 and 12th Grades
Duration: 40-60 hours
Fee: $1500